Regions Of Different Conductivity Research Articles

Maxwell–Wagner relaxation in the CaMn7O12 perovskite

Abstract In this work we have measured the complex dielectric permittivity of a polycrystalline material using samples of different thickness (frequency range 20–1 MHz). The results reveal that the CaMn 7 O 12 material is electrically heterogeneous as it consists of regions of different conductivities. In this kind of electrically heterogeneous materials the variation of the dielectric permittivity as a function of temperature can be fitted to a Maxwell–Wagner model. In the case of the CaMn 7 O 12 sample this model fits only partially the experimental data and we need to include three regions of different conductivities to explain the obtained dielectric response.

Using the vector potential in evaluating the likelihood of peripheral nerve stimulation due to switched magnetic field gradients.

The time-varying magnetic field gradients used in MRI can cause peripheral nerve stimulation (PNS) in human subjects, as a result of the electric fields induced in tissue. The local electric field, E, is given by E = - partial differential A/ partial differential t - nabla phi where A, is the vector potential and phi is the scalar electric potential generated by charges accumulated at boundaries between regions of different conductivity. Difficulties in calculating phi have led some investigators to use - partial differential A/ partial differential t alone as a predictor of the induced field. Here the spatial variation of - partial differential A/ partial differential t and E is investigated for the case of a simple spherical conductor exposed to time-varying gradients produced by two different gradient coils that generate identical internal magnetic fields, but very different vector potentials. The results indicate that the temporal derivative of A bears little relation to the induced electric field, and that consequently neglecting the effect of the scalar potential introduces significant errors in estimating the likelihood of PNS.

Current–voltage and imaging of TiSi2 islands on Si(001) surfaces using conductive-tip atomic force microscopy

Using conducting tip atomic force microscopy (c-AFM), we have measured the current–voltage (I–V) characteristics of individual submicron islands of TiSi2 on Si(100) surfaces, and we have developed an imaging approach that distinguishes the electrical properties of the islands. The Schottky barrier height (SBH) of the submicron TiSi2 islands was deduced from the I–V measurements. The results indicate that there is a significant variation of SBH among the islands on the same surface. The measurements employ a conventional AFM with a heavily B-doped diamond tip to obtain the current–voltage relations. In contact mode AFM, electrical signals are extracted independently from the topographic image. In addition, we have modified the imaging method to probe the local electrical properties of a surface with regions of different conductivity. Using a lock-in technique both phase and amplitude images were obtained, and the resultant image is essentially a map of the differential surface conductivity. Using this method, TiSi2 islands on a Si(100) surface were imaged. This approach can be readily extended to other materials systems.

Investigation of ion-bombarded conducting polymer films by scanning electrochemical microscopy (SECM).

Scanning electrochemical microscopy (SECM) was used to investigate the effect of ion bombardment on thin films of the conducting polymers poly[3-ethoxy-thiophene] (PEOT) and poly[ethylenedioxy-thiophene] (PEDT). Bombardment with Ar+-ions converts the topmost 30 nm thick layer to an essentially insulating material. SECM approach curves as well as two dimensional scans prove the existence of regions of different conductivity within the irradiated regions that did not show a significant dependence on ion dosage. PEDT layers patterned by ion bombardment through microscopic masks are investigated as prototypes of miniaturized printed circuit boards that can be formed by galvanic copper deposition onto conducting PEDT. Defects in conducting polymer patterns were analyzed by SECM imaging before any deposition of copper. Appropriate representations of SECM images for the evaluation of this technologically important question are discussed.

Anatomically constrained electrical impedance tomography for anisotropic bodies via a two-step approach

Discusses the inclusion of anatomical constraints and anisotropy in static Electrical Impedance Tomography (EIT) using a two-step approach to EIT. In the first step, the boundaries between regions of different conductivities are anatomically constrained using Magnetic Resonance Imaging (MRI) data. In the second step, the conductivity values in different regions are determined. Anisotropic conductivity regions are included to allow better modeling of the muscle regions (e.g., skeletal muscle) which exhibit a greater conductivity in the direction parallel to the muscle fiber. This two-step approach is used to reconstruct the conductivity profile of a canine torso, illustrating its potential application in extracting conductivity values for bioelectric modeling.

Application of the boundary element method to the solution of anisotropic electromagnetic problems

The paper discusses the application of the boundary element method to the computation of the electric potential and magnetic field generated by bioelectric sources in an anisotropic inhomogeneous volume conductor, using a proper coordinate transformation. It is shown that the co-ordinate transformation generally not only affects the conductivity and geometry of the volume conductor under consideration, but also the current source term and the continuity relation on the interfaces bounding regions of different conductivity. To illustrate these results, the electric potentials in an anisotropic finite length cylinder and in an anisotropic volume conductor of irregular (torso) shape, computed by the boundary element method, are compared with the results obtained by the analytical solution and the finite element method, respectively.

Describing head shape with surface harmonic expansions

Surface harmonic expansions are used to represent boundaries between regions of different conductivity in the human head. This facilitates calculation of the electric potential and magnetic field generated by neural current sources using discretized integral equations.

Quantitative formulations of electrophysiological sources of potential fields in volume conductors.

The noninvasive measurement of electrical potentials at the surface of the body (e.g., the electrocardiogram) has long been considered an important tool in clinical diagnosis. Electrophysiological modeling and simulation is valuable as an aid in the interpretation of such potential recordings. In all cases, the potential field can be considered to arise from bioelectric sources operating in a volume conductor. This paper concentrates on the appropriate quantitative formulation for these sources. Such sources arise from excitable cells undergoing action potentials (primary sources) or at passive boundaries between regions of different conductivity (secondary sources). These sources are described and discussed for arbitrary cell shapes, circular cylindrical cells, conductive media with piecewise constant conductivity, and for syncytial tissue whose macroscopic properties are anisotropic.

On the finite difference solution of two-dimensional induction problems

Summary The numerical solution by finite differences of two-dimensional problems in electromagnetic induction is reexamined with a view to generalizing the method to three-dimensional models. Previously published work, in which fictitious values were used to derive the finite difference equations, is discussed and some errors in the theory which appear to have gone undetected so far, are pointed out. It is shown that the previously published B-polarization formulas are incorrect at points where regions of different conductivity meet, and that the E-polarization formulas are inaccurate when the step sizes of the numerical grid around the point are uneven. An appropriately-modified version of the two-dimensional theory is developed on the assumption that the Earth's conductivity is a smoothly-varying function of position, a method which naturally lends itself to three-dimensional generalization. All the required finite-difference formulas are derived in detail, and presented in a form which is suitable for programming. A simple numerical calculation is given to illustrate the application of the method and the results are compared with those obtained from previous work.

The Perturbation of Alternating Geomagnetic Fields by Three-dimensional Island Structures

Summary The perturbation of alternating geomagnetic fields by island-type structures in three dimensions is considered. Two different structures are studied for sinusoidally time-varying source fields of three different frequencies. The general model is that of a semi-infinite conducting half-space with regions of different conductivities. A single-island model and a two-island model are considered. The equations and boundary conditions are solved by a numerical method and the results are compared between models. Contour plots of the amplitudes of the E and H components over the surface of the conducting region are compared near the islands. Profiles of the amplitudes of the E and H components are also given so that the values of the contours may be specified. Profiles of phase are given so that the sign of the observed E and H components at any particular instant in time may be compared. The distortion of the current lines and associated fields by island structures is illustrated in the results. Also, phase changes of the components due to the island structures are evident. The results indicate that a second smaller island near a larger island considerably modifies the fields associated with the larger island.

Induction in a Non-Uniform Conducting Half-Space by an External Line Current

Summary A two-dimensional problem in electromagnetic induction which is of interest in explaining the effect of a coastline on geomagnetic variations is solved analytically. The model considered consists of a periodic line current above a non-uniform earth, represented by a conducting half space with a horizontal plane boundary and divided by a vertical plane into two regions of different conductivities. The solution for the field is generated by perturbation from the corresponding solution for a perfectly conducting earth. Limiting expressions for the field are derived for the case when the height and magnitude of the line current approach infinity in such a way that the inducing field near the Earth becomes uniform and finite. The variation of the field at the surface of the conductor is shown for a line current at finite height and the variations at different heights above the conductor are shown for a uniform inducing field. The latter results are compared with those recently obtained by numerical methods.

Apparent Resistivity Calculations for Three Two-dimensional Conductivity Models with Vertical Discontinuities

Electromagnetic induction in three two-dimensional models of conductors with two regions of different conductivity is considered. Solutions are obtained for both the H-polarization and E-polarization cases by a numerical method. Apparent resistivity as a function of period is plotted for various locations relative to the surface contact. For the H-polarization case, the apparent resistivity values calculated for points near the surface contact are affected by the varying surface charge on the interface between the regions, and a value different from the expected value is obtained. In the E-polarization case the apparent resistivity curves exhibit a "dip" characteristic when the apparent resistivity is calculated for surface points near a shelf or step structure. In both cases the value of apparent resistivity calculated at or near surface contacts between different conducting regions depends greatly on the sub-surface structure.

The Effect of Finite Metal Conductivity on the Condensation Heat Transfer to Falling Water Rivulets on Vertical Heat-Transfer Surfaces

An analytical study has been made of the condensation of vapor onto falling rivulets of liquid which are constrained in lateral width by vertical non-wetting Teflon stripes on a flat metal heat-transfer surface. Under the condition studied it is shown that finite metal conduction plays a primary role in limiting the overall heat-transfer coefficient because in any system (drops or rivulets) where a triple point of metal, vapor, and liquid exists, the zero water path at the triple point would provide an unlimited conductance of heat were it not for finite metal conductivity or interfacial resistance. In the present paper, the temperature field and heat flow in a liquid rivulet and the underlying metal are computed using finite-difference methods. The metal plate is of constant thickness but the liquid rivulet is bounded by an arc of a circle as dictated by surface tension. The system involves two connected regions of different conductivity and shape, and the entire network is solved by an over-relaxation process taking into account the discontinuity in temperature gradient at the liquid-metal junction. Results are related to the practical application of such a system in desalination processes. The work was supported by the Office of Saline Water, Department of the Interior.

Magnetic field behaviour near conductivity discontinuities and possible inferences from geomagnetic local gradients

The influence of the underground conductivity structure on the horizontal geomagnetic local gradient is discussed. The conductivity distribution is assumed to be two-dimensional with an infinite vertical boundary between the regions of different conductivity. In these cases the local gradient in geomagnetic variations increases discontinuously when crossing the boundary, and the magnitude of the increase is proportional to the difference of conductivities of the regions at both sides of the boundary. These circumstances make it possible to determine the conductivity difference by measuring the local gradient of geomagnetic variations and the telluric field. The limitations of the method are discussed. Furthermore, it is shown, that the telluric field should be measured over long rather than short paths.

A Mathematical-Physical Model of the Genesis of the Electrocardiogram

A fundamental problem of cardiac electrophysiology is that of relating quantitatively the electrical activity within the heart to the complete timevarying potential distribution at the body surface. A new numerical method is described for the calculation of the surface potential on an irregularly shaped closed external surface due to an arbitrary source distribution in a medium containing regions of different conductivity, subject to the appropriate boundary conditions. The method is intended to provide an exact theoretical analysis of the experimental data acquired by A. M. Scher and others who have been mapping the pathways of ventricular depolarization in dogs and other animals. In anticipation of the above research program, a number of exploratory computations are reported. For example, the surface potential distribution has been calculated for a cylinder of human torso cross-section with a hemispherical dipole layer current source in approximate heart position and orientation and containing "lungs" of conductivity different from that of the surrounding medium. Under certain conditions, when lung-like inhomogeneities are introduced, a simple dipole source can generate a potential distribution having the multiple maxima and minima characteristic of higher multipole sources.